Imbalanced ball's affect on static friction

[Disgrntld]

Given a circle with a point mass attached, what is the relationship between the linear force and the force of static friction as it rolls without slipping? Each force diagram I made (http://imgur.com/a/xK8i1) seems a plausible place to start: a makes no torque, b makes no linear force, c makes no static friction.

 

[mikeph]

Is the circle massive? What do you mean by "linear force"?

 

[mfb]

I would try to calculate torque in the system of the circle.
There are many ways to split the gravitational attraction in two parts.

 

[Disgrntld]

MikeyW, I'm interested in the generic case, just some circle of radius r. I honestly don't know how the size would affect it, but if the dynamics of the system change past some massive size, I'm interested in the smaller case. By linear force, I meant forces parallel to the slope of the ground that would result in sliding if there was no friction.

mfb, ok, so if I try to focus on how the particle generates torque on the circle, I'm thinking it would be easiest to split the force along the line through the center of mass like this (http://i.imgur.com/Ip7n7.png). The force vector perpendicular to a multiplied by r gives us the amount of torque. However, what do I do with a now? It causes no torque on the circle, but it's not parallel to the slope.

What I really want to understand are the interplay of forces here that would allow a situation like this (http://i.imgur.com/XpZPu.png) to have no angular or linear acceleration.

 

[mfb]

"massive" refers to "does it have mass", not its size. I think without any mass, your pointmass would simply fall down vertically until it reaches the slope (and the circle moves away in an undefined way) and continue sliding afterwards.

 

[Disgrntld]

Oh, yes, the circle has mass. That was silly of me.